7th International Conference from “Scientific Computing to Computational Engineering” 7th IC-SCCE Athens, 6-9 July, 2016 © LFME
THERMAL AND OPTICAL INVESTIGATION OF A U-TYPE EVACUATED TUBE COLLECTOR WITH A MINI-COMPOUND PARABOLIC CONCENTRATOR AND A FLAT ABSORBER D. Korres1, C. Tzivanidis1, J. Alexopoulos1, G. Mitsopoulos1 1
National Technical University of Athens, Athens, Zografou, 157 73, Greece, e-mail:
[email protected]
Keywords: Solidworks, Mini-CPC, evacuated tube, optical efficiency, flow simulation, convection, thermal performance. Abstract. In this analysis a U-type evacuated tube with a CPC reflector and a flat absorber is investigated thermally and optically. The collector was simulated and analyzed in ten different inlet water temperatures (10÷100 oC per 10 oC) for zero slope, while the solar incident angle (Θ) was considered to be zero for the thermal analysis part. Firstly, the thermal efficiency was calculated and compared to the respective of a flat plate collector. Moreover, the overall heat loss coefficient of the collector as well as the temperature fields of the absorber, the cover and the water were determined in each case. In addition, the convection between the water and the tube was studied and validated by a theoretical model. Finally, the optical efficiency was examined in several transversal and longitudinal solar incident angles. Solidworks and its program ‘’Flow simulation’’ were used for designing and the simulating the collector.
1 INTRODUCTION The concentrated solar collectors as well as the evacuated tube ones are of considerable interest since can support a wide range of both domestic and industrial applications. The most well-known of these categories are the parabolic trough (PTCs), the compound parabolic (CPCs) and the U-pipe evacuated tube collectors (ETCs). There not many studies have conducted in how such systems perform. For instance, C. Tzivanidis et al [1] investigated the thermal and the optical performance of a parabolic trough collector for several different operating conditions while Z.D. Cheng et al analyzed a PTC optically [2] and developed a new modeling method for concentrating systems [3] by using the Monte Carlo ray-tracing method. Moreover, Chung-Yu Tsai and Psang Dain Lin [4] optimized a variable focus parabolic trough concentrator and compared it to the classical PTC and the semi-cylindrical configuration. Compound Parabolic Collectors have, also, barely been examined with numerical models and simulation tools. Bellos et al. [5] designed a compound parabolic collector, examined the thermal performance of it and optimized its optical behavior with Solidworks. Souliotis et al [6] analyzed asymmetrical cpc for integrated solar systems with one tank inside the collector. In addition, Hamdi Kessentini and Chiheb Bouden [7] developed a numerical model to study the thermal performance of a double tank integrated collector storage system (ICS) accompanied by asymmetric CPC reflectors. As far the evacuated tube collectors are concerned there is a variety of different designs the main of which are the Heat Pipe, the Counter-Flow and the U-tube configuration. Xinyu Zhang et al [8] examined the performance of a direct flow coaxial (counter flow) evacuated tube collector with and without a heat shield and found that the collector performs better with the shield, while S. Ataee and M. Ameri [9] conducted an energy and exergy analysis of a similar collector. L.M. Ayompe and A. Duffy [10] made a thermal performance analysis of a heat pipe evacuated tube system while Hongfei Zheng et al [11] studied on how the emissivity of the back receiver’s surface influences the heat losses of a heat pipe application. The U-pipe system has, also, been investigated. Y. Gao et al [12] put forward a mathematical model so as to describe the thermal behavior of a U-pipe evacuated tube collector while Liangdong Ma et al [13] conducted a thermal investigation on a U-type evacuated tube application by analytical method. Y. Kim and T. Seo [14] examined numerically the performance of four different-shaped evacuated tube collectors (one counter flow and three U-tubes with several absorber configurations). A combination of the ETC and CPC technology appears on study [15] where two different CPC reflectors are applied on a U-shape evacuated circular absorber in order to determine the system’s efficiency. Gang Pei et al [16], also, examined the operation of such an ETC with and without a mini compound parabolic concentrator and they found out that the concentrator enhances the thermal performance of the ETC in high temperature ranges.
D. Korres et al.
In this paper, a U-type evacuated tube collector with a mini compound parabolic concentrator and a flat absorber is simulated. First of all, the collector’s thermal performance and the overall heat loss coefficient were calculated for several operating conditions while the temperature fields of the collector were determined. The convection between the water and the U-pipe was examined and verified by a theoretical model that considers constant temperature on the walls. Finally, the optical efficiency was determined for several solar incident angles.
2 DESIGN OF THE COLLECTOR The design and the main dimensions of the collector are depicted on Fig. 1.
Figure 1. U-type evacuated tube collector with a flat absorber and a CPC reflector
From Fig. 1 we see that the collector consists of a U-pipe, a flat absorber with two circular receptors for the straight parts of the U-pipe, a glass tube inside of which vacuum regime prevails and a CPC reflector. The geometry of the reflector differs from the classical compound parabolic concentrators’ design. Particularly, the difference here is that each of the two identical parabolas (C and D) that form the reflector’s profile has its focus at the same symmetry side the parabola curve is. This leads to the formation of complete reflector geometry without the need of an involute in the region between the vertex points. The focuses of the parabolas are located on the centerlines of the straight parts of the U-tube while the focal distances are perpendicular to the aperture plane, something that renders our collector optimized for zero inclination angles (Θ = 0o). The next table gives the material, the thicknesses and the main properties of the collector’s components. Component
Material
Thickness(mm)
Glass tube Absorber & tube Reflector
Glass Copper Aluminum
1 0.2 & 1 1
Thermal properties εg =0.88 εp = 0.1 ̶
Optical properties Transmittance: τ = 1 Absorptance: α = 0.8 Reflectance: ρ=1
Table 1. Main characteristics of the collector’s components The problem’s data are given below: Variable Environment temperature Inlet water temperature range Water mass flow rate Wind heat transfer coefficient Global irradiance
Symbol Tα Ti
m hw GT
Table 2. Problem’s data
Value 10 10-100 0.0025 10 1000
Units °C °C kg/s W/m2/K W/m2
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3 THERMAL ANALYSIS The thermal performance of the collector is being examined on ten different operating points (Ti=10,20,30,40,50,60,70,80,90 and100 oC) considering that the global irradiance (GT) is constant and perpendicular to the aperture plane. The determination of the overall heat loss coefficient, the thermal efficiency and the convection regime inside the U-pipe are the main aspects examined on this chapter. Bellow, the equations of the thermal analysis part are presented:
Qu m C p To Ti h f As Ts T f Qp,0 QL , UL
(1)
QL 1 , Tp Ta Ap
(2)
Ap σ Tp4 Tg4 QL , 1 1- ε g Ap εp εg Ag Q Qu Qu , th u Qs Aa GT La W GT
(3)
(4)
Equation (1) expresses the water heat gain while (2) presents the overall heat loss coefficient. The overall heat losses which in our case are equal to the top heat losses are given in (3) while (4) shows three expressions of the collector’s efficiency. Qp,Θ=0ο in equation (1) is the whole thermal power that reaches the absorber’s surface. Equation (3) holds considering diffusive radiation heat exchange between two specific grey bodies’ surfaces, a semi-cylindrical and a flat one, which form an enclosure [17]. Bodies in Solidworks are considered as grey while thermal radiation approximates the diffusive behavior. 3.1 Thermal performance (ηth) In Fig. 2 the thermal performance of our collector is depicted and compared to the efficiency of a selective flat plate collector with the same optical losses and operating conditions (study [18]). 0.9
Thermal efficiency (ηth)
0.8 0.7 0.6 0.5
η_FPC
0.4
η_ETC
0.3 0.2 0.1 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
(Ti-Tα)/GT (m2 K/W) Figure 2. Thermal efficiency The figure above declares the declination of the efficiency which is caused due to the increment of the heat losses as Ti increases while the FPC’s efficiency decreases abruptly compared to the examined collector because of the vacuum regime that prevails inside the glass tube of the last one.
D. Korres et al.
3.2 Overall heat loss coefficient (UL) In this paragraph the overall heat loss coefficient’s curve is presented.
0.9
UL (W/m2/K)
0.8
0.7 UL
0.6 0.5
0.4 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (Ti-Tα)/GT (m2 K/W) Figure 3. Overall heat loss coefficient’s curves
The UL curve comes from the combination of equations (2) and (3):
σ Tp4 Tg4 1 UL , 1 1- ε g Ap Tp Ta εp ε g Ag
(5)
From Fig. 3 we observe that the overall heat loss coefficient increases with Ti something that happens due to the receiver’s temperature (Tp) increment.
T (°C)
3.3 Temperature fields The temperatures of the inlet and the outlet water as well as the average temperature values of the tube, the receiver, the glass tube and the water are depicted on the next figures as a function of the inlet water temperature. 110 100 90 80 70 60 50 40 30 20 10 0
To Ti
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (Ti-Tα)/GT (m2 K/W) Figure 4. Inlet and outlet water temperatures.
Fig. 4 shows that the temperature difference from the inlet to the outlet (Τo-Τi) does not affected significantly by the inlet water temperature increment. This happens because the energy per unit time absorbed in the plate (αˑQp,Θ=0˚) is constant and the overall heat losses are very low compared to this absorber’s heat gain due to the negligible convection inside the glass tube.
D. Korres et al.
T (°C)
110 100 90 80 70 60 50 40 30 20 10 0
Tp Ts Tf Tg
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (Ti-Tα)/GT (m2 K/W) Figure 5. Average absorber, glass and water temperatures.
It is obvious from Fig. 5 that a big divergence between the cover’s and the rests’ temperatures occurs while the Tp, Ts and Tf curves seem to be parallel among them. The reason for this is the negligible overall heat losses as well as the fact that the Tp-Tf temperature difference is affected directly by Τo-Τi as equation (1) suggests. 3.4 Convective heat transfer coefficient (hf) The first thing we have to mention in this paragraph is that the water flow inside the tube was considered as laminar due to the low velocity fields and fully developed since the tube’s length is much greater than the inner diameter of it. The convective heat transfer coefficient is calculated by solving equation (1) as bellow:
hf
m C p To Ti As Ts T f
,
(6)
The simulation results were validated through the model from convective heat transfer theory of equation (7) that follows considering constant temperature at the inner tube walls:
h f_T
0.0668 Re Pr Dt,i / Lt k f , = 3.66 + 2/ 3 Dt,i 1+0.04 Re Pr D / L t,i t
Re and Pr were taken for the mean water temperature of each case.
hf (W/m2/K)
The values of
(7)
hf_simulation hf_theoretical(T=ct)
550 530 510 490 470 450 430 410 390 370 350 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (Ti-Tα)/GT (m2 K/W)
Figure 6. Water to tube heat transfer coefficient’s curve As we can see from Fig. 6 the convection heat transfer coefficient increases with Ti as we expected. The simulation curve is successfully validated from theory since the divergence of the two solutions seems to be constant and does not exceed 2.6%.
D. Korres et al.
4 OPTICAL ANALYSIS In this chapter the optical performance of our collector is studied for several different operating conditions. In particular, the collector’s operation will be tested at various longitudinal and transversal solar incident angles.
Figure 7. Transversal and longitudinal angle of incidence On the above figure the longitudinal and the transversal angles of incidence (ΘL and ΘT) are introduced while the optical efficiency is given by the following equation:
opt ,Θ
Q p ΘL ,ΘT QS
Q p ,Θ QS
,
(8)
On the above equation, Qp is the total energy per unit time that reaches the absorber’s surface. 4.1 Optical efficiency of the collector (ηopt) In the next figure the optical performance of the collector as a function of the longitudinal and the transversal angles of incidence is presented.
Figure 8. Optical performance as a function of a) the transversal and b) the longitudinal angle of incidence. The optical efficiency of the collector decreases as the incident angles take greater values something that has to do with the optimization of the collector for zero incident angles. Hence, the whole incident radiation goes on the absorber only when the incident angle (Θ) takes values near to 0o. The reason why the ΘL curves are smoother than the ΘT ones is that all the longitudinal rays which are incident on the active part of the reflector are bound to reach the focuses.
D. Korres et al.
5 CONCLUSIONS In this study the optical and the thermal behavior of a U-Type ETC with a mini CPC reflector and a flat absorber was investigated and analyzed. The following conclusions come to complete the study and make clear the important points of our analysis. The collector’s thermal efficiency (Fig. 2) decreases slightly with Ti due to the increment of the overall heat losses. Also, the slope of the efficiency curve is much lower compared to the flat plate one since the convection inside the glass chamber is negligible. The overall heat losses coefficient (Fig. 3) increases with Ti due to the absorber’s temperature increment. The Τo-Τi and Τp-Τf temperature differences (Figs. 4 and 5) seem to be steady as Ti increases because the absorber heat gain is constant and much higher than the thermal losses due to the vacuum regime, while the glass temperature is much lower than the absorber’s one for the same reason. The reliability of our simulation is being confirmed through the validation of the convective heat transfer coefficient by a specific model of heat transfer theory since the maximum divergence between the two solutions was found to be 2.6% (Fig.6). According to Fig. 8 the optical efficiency decreases with ΘT and ΘL increment since the collector has been optimized for Θ = 0o. The longitudinal angle of incidence (Fig. 8b) seems that affects the optical efficiency more gently than ΘT does providing a smoother efficiency curve.
NOMENCLATURE General parameters
Greek symbols 2
A Cp D GT
Surface area, m Fluid specific heat, kJ/(kg K) Diameter, m Incident solar radiation per unit area, W/m2
hf
Water to tube heat transfer coefficient, W/(m2 K)
hf_Τ
Water to tube heat transfer coefficient for Ts=ct, W/(m2 K)
hw
Wind heat transfer coefficient, W/(m2 K)
kf
Water thermal conductivity, W/(m K)
L 𝑚̇ QL
Length, m Mass flow rate, kg/s Overall heat losses, W
Qp
The total solar power that reaches the receiver, W
QS
Solar heat flow rate on the aperture, W
Qu UL W
Useful thermal power, W Overall heat loss coefficient, W/(m2 K) Aperture width, m
T
Temperature, °C
Tf
Mean water temperature, °C
Dimensionless numbers Pr Re
Prandtl number Reynolds number
α ρ ε η σ
Absorptance Reflectance Emittance Efficiency Boltzmann constant, W/(m2 K4)
τ
Transmittance
Θ
Angle of incidence, (°)
Subscripts α
Ambient
a
Aperture
g
Glass
i
Inlet water for temperature (T) Inner for diameter (D)
L
Longitudinal (for Θ)
o opt
Outlet water for temperature (T) Optical
p
Absorber
s
Inner tube wall
T t th
Transversal (for Θ) U-tube Thermal
D. Korres et al.
REFERENCES
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